Problem: Simplify the following expression: $ r = \dfrac{4}{5} + \dfrac{-9}{t + 7} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{t + 7}{t + 7}$ $ \dfrac{4}{5} \times \dfrac{t + 7}{t + 7} = \dfrac{4t + 28}{5t + 35} $ Multiply the second expression by $\dfrac{5}{5}$ $ \dfrac{-9}{t + 7} \times \dfrac{5}{5} = \dfrac{-45}{5t + 35} $ Therefore $ r = \dfrac{4t + 28}{5t + 35} + \dfrac{-45}{5t + 35} $ Now the expressions have the same denominator we can simply add the numerators: $r = \dfrac{4t + 28 - 45}{5t + 35} $ $r = \dfrac{4t - 17}{5t + 35}$